Suppose the Chazan starts saying Kaddish in error instead of saying Tachanun - should the Chazan just stop saying Kaddish? Is there a break off point that up to there you stop saying Kaddish and beyond that you just finish it already? Suppose the Chazan finished Kaddish do you say Tachanun now or do you just skip it at this point? (sources)

Halichos Shlomo Tefila Perek 11 Os 2 says that if the error was noted in the middle of Kriyas HaTorah then after Kriyas HaTorah, Tachanun should be recited immediately. (no mention regarding saying or not saying Chatzi Kaddish again)

Orchos Rabbenu Volume 3 Page 225 mentions a story that happened by the Chazon Ish where the Chazan said Kaddish in error, and the Chazon Ish said to just skip saying Tachanun.

Naharei Aish Likutei Diburim 69 mentions that the Satmer Rabbi - Rabbi Yoel Teitelbaum Zatzal - would not say Tachanun on a day where there was a Yarzheit and a Seuda was being held in conjunction with that Yahrzheit. However if there was no Seuda being held in conjunction with that Yahrzheit then he would say Tachanun. Once there was a Yahrzheit where no Seuda was being held in conjunction with it and the Chazan said Kaddish, skipping Tachanun. He told everyone to immediately say Tachanun at that point. (no mention regarding saying or not saying Chatzi Kaddish again)